I learned about the philosopher Zeno of Elea from Douglas Hofstadter's Gödel, Escher, Bach. He was famous for coming up with several paradoxes. Here's a neat one:

"In a race in which the tortoise has a head start, the swifter-running Achilles can never overtake the tortoise. Before he comes up to the point at which the tortoise started, the tortoise will have got a little way, and so on ad infinitum.
-- Internet Encyclopedia of Philosophy"

He had a related paradox which stated that motion was inherently impossible. I like using this one when my wife wants me to empty the trash or something else which requires movement.

Anyone with a little bit of math expertise can easily debunk that "paradoxon", though. :) Both the distance and duration of each iteration approach zero, so for an infinite amount of time the duration of each iteration becomes infinitely short. In fact, the duration of the iterations decreases so quickly that even an infinite amount of these infinitely short timespans only adds up to a finite amount of time.